Cosmological Constraints from the Redshift Cosmological Constraints from the Redshift

Dependent of the Alcock-Paczynski TestDependent of the Alcock-Paczynski Test

Xiao-Dong Li (Xiao-Dong Li (李霄栋李霄栋 ), KIAS), KIAS

WITH Changbom Park &WITH Changbom Park &

Cristiano G. Sabiu, Hyunbae Park, David H. Weinberg,Cristiano G. Sabiu, Hyunbae Park, David H. Weinberg,

Donald P. Schneider, Juhan Kim, Sungwook HongDonald P. Schneider, Juhan Kim, Sungwook Hong

The 7The 7thth KIAS Workshop on Cosmology and Structure Formation KIAS Workshop on Cosmology and Structure Formation

What: AP, the shape distortion of objects/structures,

due to wrong cosmology (adopted to compute r(z))

How: AP distortion is less significant than RSD, but more evolves with redshift.

We focused on the redshift dependence, to probe AP and avoid RSD.

Result: We applied our idea to BOSS DR12 galaxies and obtained very

tight cosmological constraint.

Combined:

Ωm = 0.301 ± 0.006

w = -1.054 ± 0.025

Li et al. 2016, ApJ accepted arXiv:1609.05476

SN

OurBAO+H0

CMB

∆θ

∆z

• The Alcock-Paczynski TestThe Alcock-Paczynski TestAlcock & Paczynski, Nature 281, 358 (1979)Alcock & Paczynski, Nature 281, 358 (1979)

AP = Apparent shape distortion if H, DA are wrong.

The Alcock-Paczynski (AP) effect refers to the geometirc distortion when incorrect cosmological models are adopted for transforming redshift to comoving distance.

True

Patten

Distorted

Pattern

Viewpoint from Viewpoint from ΛCDM oΛCDM observerbserver

Incorrect cosmology → shape distortion Incorrect cosmology → shape distortion – and, the distortion is redshift dependentand, the distortion is redshift dependent

The Alcock-Paczynski Test The Alcock-Paczynski Test

Q: How can we find isotropic objects in the Universe?

A: Large scale distribution of galaxies!A: Large scale distribution of galaxies!

Credit: Sloan Digital Sky Survey.

Problem of RSD

Redshift Space Distortion (RSD) produces serious anisotropy Redshift Space Distortion (RSD) produces serious anisotropy

Difficult modeling (NL clustering)Difficult modeling (NL clustering)

Galaxy distribution in real space

Galaxy distribution in redshift space

RSD effects RSD effects on 2-point correlation function along (on 2-point correlation function along () & across () & across () LOS) LOS

Horizon-Run 4 Horizon-Run 4 (Kim et al. 2015, JKAS, 48, 213)(Kim et al. 2015, JKAS, 48, 213)

Our Option: the redshift dependenceOur Option: the redshift dependence

RSDRSD

Kaiser effects on large scales and FoG Kaiser effects on large scales and FoG

effects on small scales effects on small scales

(pattern ~ independent of redshift)(pattern ~ independent of redshift)

AP DistortionAP Distortion

Pattern evolves with distancePattern evolves with distance

True

Patten

Distorted

Pattern

Viewpoint from Viewpoint from ΛCDM oΛCDM observerbserver

Incorrect cosmology → shape distortion Incorrect cosmology → shape distortion – and, the distortion is redshift dependentand, the distortion is redshift dependent

The Alcock-Paczynski Test The Alcock-Paczynski Test

Redshift Evolution of APRedshift Evolution of AP

How much How much

radial stretch radial stretch

at different z?at different z?

[Viewpoint from [Viewpoint from

ΩΩmm=0.31 ΛCDM =0.31 ΛCDM

oobserver]bserver]

stretchstretch

compressioncompression

Proof-of-concept on HR3 N-body: Proof-of-concept on HR3 N-body: Gradient FieldGradient FieldX.-D. Li, Changbom Park, J. E. Forero-Romero, Juhan Kim 2014 ApJX.-D. Li, Changbom Park, J. E. Forero-Romero, Juhan Kim 2014 ApJ

We study the gradient field of the spatial distribution of galaxies.We study the gradient field of the spatial distribution of galaxies.

The anisotropy (quantified by the mean direction of gradient vectors) has redshift dependence The anisotropy (quantified by the mean direction of gradient vectors) has redshift dependence

in case of adopting wrong cosmologies.in case of adopting wrong cosmologies.

Mean of Mean of

cosine of cosine of

vector vector

directiondirection

Proof-of-concept on HR3 N-body: Proof-of-concept on HR3 N-body: 2pCF2pCFX.-D. Li, Changbom Park, Cris G. Sabiu, Juhan Kim 2015 MNRASX.-D. Li, Changbom Park, Cris G. Sabiu, Juhan Kim 2015 MNRAS

θθss

r(z)r(z)

=cos θ=cos θ

RSD, No APRSD, No AP: :

anisotropic, but no anisotropic, but no

significant redshift significant redshift

evolutionevolution

RSD & APRSD & AP: :

Redshift EvolutionRedshift Evolution

No RSD, No APNo RSD, No AP: :

IsotropicIsotropic

II. Application to

BOSS DR12 Samples~1/4 sky, ~1/4 sky, z ~z ~ 0.15-0.7, 0.15-0.7,

~1.3 million galaxies ~1.3 million galaxies

Application to BOSS DR12 galaxiesApplication to BOSS DR12 galaxiesX.-D. Li, Changbom Park, C.G. Sabiu, et al., to appearX.-D. Li, Changbom Park, C.G. Sabiu, et al., to appear

LOWZ 8,337 deg LOWZ 8,337 deg 22 . CMASS 9,376 deg . CMASS 9,376 deg 22 (~1/4 sky) (~1/4 sky)

~1.13 M gals at 0.15 ~1.13 M gals at 0.15 ≤≤ z z ≤≤ 0.7 0.7

SystematicsSystematics

1. RSD1. RSD (still the most significant)(still the most significant)

2. Galaxy bias2. Galaxy bias

(affect clustering)(affect clustering)

3. Angular variation3. Angular variation

4. Radial variation4. Radial variation (incomplete LF coverage)(incomplete LF coverage)

5. Fiber collision 5. Fiber collision (high-density (high-density

regions under-sampled)regions under-sampled)

We create mock surveys to We create mock surveys to

model the observational artifactsmodel the observational artifacts

Horizon run Horizon run NN-body-body

HR3 HR3 (Kim et al. 2012) (Kim et al. 2012)

(10.815 (10.815 hh−1−1 Gpc) Gpc)33

7120712033 particles particles

WMAP5 CosmologyWMAP5 Cosmology

72 mocks → covariance estimation72 mocks → covariance estimation

HR4HR4 (Kim et al. 2015) (Kim et al. 2015)

(3.15(3.15hh−1−1 Gpc) Gpc)33

6300630033 particles particles

WMAP5 CosmologyWMAP5 Cosmology

4 mocks → modeling systematic4 mocks → modeling systematic

MultiDark-Patchy MocksMultiDark-Patchy Mocks

2048 mocks → covariance 2048 mocks → covariance

0.15 < z < 0.7; Six 0.15 < z < 0.7; Six zz-bins-bins

1. Adopt a 1. Adopt a r(z)r(z) [ [in some cosmology],in some cosmology], construct 3D LSS construct 3D LSS

2. Measure 2. Measure ξξ(s, (s, μμ)) in each in each zz-bin -bin

3. Quantify the evolution [3. Quantify the evolution [ξ ξ from 5 high-z bins compared to the lowest redshiftfrom 5 high-z bins compared to the lowest redshift]]

Wrong Cos. → Large redshift evolution → DisfavoredWrong Cos. → Large redshift evolution → Disfavored

4. Try different cosmologies and repeat 1-3 → Cosmological Constraints4. Try different cosmologies and repeat 1-3 → Cosmological Constraints

MethodologyMethodology

LikelihoodLikelihood

Redshift evolution of 2pCFRedshift evolution of 2pCF

(comparing all redshift bins w.r.t. (comparing all redshift bins w.r.t.

the lowest redshift bin)the lowest redshift bin)

Sys. Correction from HR4Sys. Correction from HR4

Covariance from Covariance from

MDPatchy/HR3MDPatchy/HR3

2-d 2pCF in six redshift bins2-d 2pCF in six redshift bins

FOG atFOG at 11 − μ − μ → 0 and Kaiser at 1 − → 0 and Kaiser at 1 − μμ > 0.1 > 0.1

Similar to each other: Small redshift evolution of RSDSimilar to each other: Small redshift evolution of RSD

1-d 2pCF as a function of angle 1-d 2pCF as a function of angle

Focus on angular dependenceFocus on angular dependence

6 Mpc/h < s < 40 Mpc/h

Normalizing the amplitude; Normalizing the amplitude;

focus on shape [avoid sys focus on shape [avoid sys

from gal bias]from gal bias]

Observation VS SimulationObservation VS Simulation

HR4 mock reproduces observation very well

Estimating systematic Estimating systematic

Redshift evolution from RSD, and so onRedshift evolution from RSD, and so on– Small in most redshift binsSmall in most redshift bins– Relative large in the 6Relative large in the 6thth bin but still correctable bin but still correctable

Check gal biasCheck gal bias

Considering the large variation of Considering the large variation of MM, effect not significant, effect not significant

Redshift evolution from AP detected at high CLRedshift evolution from AP detected at high CL

The Redshift Evolution The Redshift Evolution

Evolution wrt lowest redshift; sys corrected

Close to 0 evolutionClose to 0 evolution

Cosmological constraintCosmological constraint

Combined:

Ωm = 0.301 ± 0.006

w = -1.054 ± 0.025

SN

Our

BAO+H0

CMB

Cosmological constraint (HR3 N-body as Covmat)

Robustness Tests

Robustness Tests

Comparing the different probes of geometryComparing the different probes of geometry

BAOBAO: : DDAA(z)/r(z)/rdd, H(z)*r, H(z)*rdd

APAP: : DDAA*H(z) *H(z)

SNIaSNIa: : DDLL(z)(z)

OurOur: : ~ d D~ d DAA*H(z) / dz *H(z) / dz

– * Simple idea, successfully overcoming RSD, powerful* Simple idea, successfully overcoming RSD, powerful

* ~Independent from other techniques (combinable)* ~Independent from other techniques (combinable)

* No complicate modeling * No complicate modeling

– * Enter small scales (6 - 40 Mpc/* Enter small scales (6 - 40 Mpc/hh) difficult for most techniques) difficult for most techniques

» A lot of information encoded in small-scale clustering!A lot of information encoded in small-scale clustering!

»

Promising application to future spectroscopic surveysPromising application to future spectroscopic surveys

Show is over.Show is over.

Thank you.Thank you.